Didn't get why one of your mappings is for normal mode and another one for quick view, but here is a way to do the switch in normal mode:
nnoremap s :if &sort == '+name'
\ | set sort=-size
\ | echo 'Sorted by size'
\ |else
\ | set sort=+name
\ | echo 'Sorted by name'
\ |endif<cr>
Version with modification date:
command! togglesort
\ :if &sort == '-size,+name'
\ | set sort=+mtime
\ | echo 'Sorted by modification date'
\ |else
\ | if &sort == '+name'
\ | set sort=-size
\ | echo 'Sorted by size'
\ | else
\ | set sort=+name
\ | echo 'Sorted by name'
\ | endif
\ |endif
nnoremap s :togglesort<cr>